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Mathematics > Dynamical Systems

Title:Local perturbations of conservative $C^1$-diffeomorphisms

Abstract: A number of techniques have been developed to perturb the dynamics of
$C^1$-diffeomorphisms and to modify the properties of their periodic orbits.
For instance, one can locally linearize the dynamics, change the tangent
dynamics, or create local homoclinic orbits. These techniques have been crucial
for the understanding of $C^1$ dynamics, but their most precise forms have
mostly been shown in the dissipative setting. This work extends these results
to volume-preserving and especially symplectic systems. These tools underlie
our study of the entropy of $C^1$-diffeomorphisms in (arXiv:1606.01765). We
also give an application to the approximation of transitive invariant sets
without genericity assumptions.

Comments:

31 pages, companion to the paper Entropy of C1 diffeomorphisms without a dominated splitting (arXiv:1606.01765)